Digital skeletons, generated by thinning algorithms, are used in the characterization and analysis of the shape of objects in binary images. Many proposed algorithms have been presented without a formal analysis, making it difficult to determine their correctness, convergence, and accuracy. A notable exception is provided by morphological thinning algorithms based on mathematical morphology. Jang and Chin have presented a precise definition of digital skeletons and a mathematical method for the analysis of morphological thinning algorithms. They used this analysis to design a new thinning algorithm. For some applications, the skeletons produced by their algorithm may be excessively branched due to insignificant details on the border of the objects. This report presents an alternative operator, defined within Jang and Chin's morphological method, that is less sensitive to such border noise.